
theorem Th31:
  for L being antisymmetric RelStr for a being Element of L, X
being set holds a = "/\"(X,L) & ex_inf_of X,L iff a is_<=_than X & for b being
  Element of L st b is_<=_than X holds a >= b
proof
  let L be antisymmetric RelStr;
  let a be Element of L, X be set;
  (a is_<=_than X & for b being Element of L st b is_<=_than X holds a >=
  b ) implies ex_inf_of X,L by Th16;
  hence thesis by Def10;
end;
